When do the r-by-r minors of a matrix form a tropical basis?

Details When do the r-by-r minors of a matrix form a tropical basis? When do the r-by-r minors of a matrix form a tropical basis?

2011-09-10

arxiv.org/abs/1109.2240v1

Mathematics

Combinatorics

Scientific paper

We show that the r-by-r minors of a d-by-n matrix of variables form a
tropical basis of the ideal they generate if and only if r<4, or r=min(d,n), or
else r=4 and min(d,n)<7. This answers a question asked by M. Chan, A. Jensen,
and E. Rubei.

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